Taxi driver Sebti Boukarit speaks about visiting with an in-person counselor for President Obama’s new health care law at a city office where Chicago taxi drivers go to renew their licenses.

CHICAGO — Like most taxi drivers, Sebti Boukarit doesn’t have health insurance. And because he works up to 12 hours a day, six days a week, he hasn’t had much time to sign up under the nation’s new health care law.

But when he arrived at a Chicago city office to renew his taxi license one recent morning, the opportunity was impossible to miss. Enrollment workers had set up a table in the waiting room to snag drivers just like him, who are among the health law’s most desired prospects.

“We have a captive audience,” said Salvador Cerna, a coordinator for the outreach campaign for Get Covered Illinois, which gave enrollment information to 50 cab drivers and began the sign-up process for 18.

As the March 31 enrollment deadline creeps closer, time is running out for supporters of the law to make up for the months of technical problems that hampered the new insurance exchanges and depressed enrollment.

The latest figures show nearly 3.3 million Americans have signed up for private insurance plans on the insurance marketplaces, about a million short of where the Obama administration had hoped to be at this stage of the rollout.

In recent weeks, the sign-up effort has evolved from a dragnet strategy to a highly targeted approach focused on people most likely to be uninsured — cab drivers, restaurant workers, artists, community college students — and where they can be found. Cab drivers have particular health care needs because of the hazard of traffic accidents and the long hours they spend sitting.

Enroll America, a nonprofit involved in the enrollment campaign, targeted cab drivers in Philadelphia and Austin and plans to expand to other cities, hoping to reach a good portion of the 233,000 taxi and limo drivers in the U.S. The Chicago effort is chasing after the city’s 12,000 drivers.

Hundreds of drivers have already enrolled in Philadelphia, said Ronald Blount, director of the Taxi Workers Alliance of Pennsylvania.

“Taxi drivers work one of the most dangerous jobs. They make very little money, and most of them don’t have health insurance,” Blount said. “This was an opportunity for them to get covered.”

Meanwhile, the workers targeting students and artists have moved into churches, art centers and park district gyms.

During his encounter at the taxi office, Boukarit agreed to start the enrollment process.

“I have to talk to my wife and choose a plan,” said Boukarit, 55, a native of Algeria who has lived in the United States for two decades and has driven a cab for 16 years. “I need insurance. I have treatment for my diabetes for almost 10 years. I need it to be covered.”

Taxi companies don’t provide health insurance. In Chicago, only about 30 percent of drivers have policies, according to one study. With average annual wages of $22,820 nationally, most would qualify for cost-lowering tax credits under the law. Others just starting out or working part time would qualify for Medicaid in states opting to expand the program.

Because drivers are prone to medical problems, health advocates are eager to get them covered and connected with primary care doctors rather than treated at higher cost in emergency rooms.